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Harnack inequalities and applications for functional SDEs driven by fractional Brownian motion. (English) Zbl 1327.60120
Summary: In this paper, Harnack inequalities are established for stochastic functional differential equations driven by fractional Brownian motion with Hurst parameter $$H<1/2$$. As applications, the strong Feller property, the log-Harnack inequality and the entropy-cost inequality are given. We also get the derivative estimate and give the corresponding Harnack inequality.
##### MSC:
 60H10 Stochastic ordinary differential equations (aspects of stochastic analysis) 60H20 Stochastic integral equations 60G22 Fractional processes, including fractional Brownian motion 34K50 Stochastic functional-differential equations
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